Solve for $x$ and $y$ using substitution. ${-5x+5y = 5}$ ${x = 4y+2}$
Solution: Since $x$ has already been solved for, substitute $4y+2$ for $x$ in the first equation. ${-5}{(4y+2)}{+ 5y = 5}$ Simplify and solve for $y$ $-20y-10 + 5y = 5$ $-15y-10 = 5$ $-15y-10{+10} = 5{+10}$ $-15y = 15$ $\dfrac{-15y}{{-15}} = \dfrac{15}{{-15}}$ ${y = -1}$ Now that you know ${y = -1}$ , plug it back into $\thinspace {x = 4y+2}\thinspace$ to find $x$ ${x = 4}{(-1)}{ + 2}$ $x = -4 + 2$ ${x = -2}$ You can also plug ${y = -1}$ into $\thinspace {-5x+5y = 5}\thinspace$ and get the same answer for $x$ : ${-5x + 5}{(-1)}{= 5}$ ${x = -2}$